The NSC(2,3) is expected to be similar to the quantity involving the anisotropic flow coefficients (\(v_2\)  and \(v_3\) ) under a linear response assumption [1]}, [2]}. In Fig. REF (c), we show the normalized symmetric cumulants coefficient as function of \(N_{\rm part}\)  for both unclustered and \(\alpha \) -clustered cases. The negative values of coefficients signify the anti-correlation relation between the two variables. We see a larger anti-correlation for the clustered case compared to the unclustered case. The coefficients for both the cases do not show significant \(N_{\rm part}\)  dependence. The NSC(2,3) for the clustered carbon is found to be three times larger than the NSC(2,3) obtained for the unclustered carbon. We find a small minimum of NSC(2,3) at \(N_{\rm part} \sim 57\) , where the values of the \(\langle \varepsilon _2^C\rangle \)  and \(\langle \varepsilon _3^C\rangle \)  are close to each other. Exploring the large anti-correlation between ellipticity and triangularity (elliptic flow and triangular flow), we can detect the \(\alpha \) -cluster effects of carbon in \({\rm C + Au}\)  collisions. It is to be noted that some earlier studies have explored the characteristics of the initial-state eccentricities and final hadron flow observables from the collisions of the clustered carbon and heavy-ions at various beam energies in the event-by-event framework [3]}, [4]}. In principle, we expect that the anti-correlation behavior should hold for both photons and hadrons, since their flow observables basically arise from the initial geometry.
